Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche All rights reserved. CHEG Special Topics in Mixing Lecture 7 Liquid-Liquid Mixing

Mixing Lecture 7Slide 2 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Uses for Liquid-Liquid Mixing Uses Contacting for Mass Transfer Single Mixer-Settler Staged Columns Products Stable Emulsions Food and Cosmetic Products

Mixing Lecture 7Slide 3 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Multiphase Systems Solid-Liquid Fixed Surface Area Gravity plays moderate role Gas-Liquid Variable Surface Area Gravity plays strong role Liquid-Liquid Variable Surface Area Gravity plays weak role Mass Transfer Similarity in mass transfer correlations

Mixing Lecture 7Slide 4 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Multiphase Flow Regimes Back-mixed Continuous (Liquid) Phase Solid-Liquid, Liquid-Liquid, Gas-Liquid Back-mixed Dispersed Phase Solid-Liquid, Liquid-Liquid Plug Flow Dispersed Phase Gas-Liquid Challenges What is the interfacial surface area? What are the film coefficients? Equilibrium Stages often used with Liquid-Liquid Systems Presumes mass transfer is fast and complete within residence time

Mixing Lecture 7Slide 5 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Liquid-Liquid Drop Breakup Key Principle - Drops have a characteristic strength that depends on drop size characterized by In a given fluid stress field, drops will break until the characteristic strength can no longer be overcome drops break down to a maximum size beyond which they will no longer break not all drops will be that maximum size there will be a drop size distribution

Mixing Lecture 7Slide 6 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Mass Transfer in Liquid-Liquid Systems Mass Transfer Rate, J Average Drop Sizes Various averages possible which differ bases on drop size distribution Sauter mean diameter, d 32 - average of surface area per unit volume of all drops Need to estimate interfacial area, a

Mixing Lecture 7Slide 7 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Drop Break-up in Low Viscosity Turbulent Flow Drop Weber Number (We) d Break-up occurs above a critical (We) d Break-up Stress in Turbulent Flow - Reynolds Stress Assume drops much larger than Kolmogoroff length scale so affected by eddies in the inertial sub-range

Mixing Lecture 7Slide 8 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Drop Break-up in Low Viscosity Turbulent Flow At drop break-up, break-up stresses balance stabilizing stresses  - local power per volume not average In stirred tanks, use power per impeller swept volume Combine to give Studies show d max  d 32

Mixing Lecture 7Slide 9 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. D max vs. Power per Mass Stirred Tanks may not be best for liquid drop dispersion wide distribution of eddy sizes and energy dissipation rates bypassing

Mixing Lecture 7Slide 10 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Equilibrium Drop Size Distribution Low to Moderate Dispersed Phase Viscosity Sauter Mean Diameter including viscosity effects (Calabrese, Wang & Bryner, 1986) 349 data sets (Rushton turbine) Cumulative Volume Frequency (Wang & Calabrese, 1986) 146 data sets

Mixing Lecture 7Slide 11 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Minimum Dispersion Speed N JD - minimum impeller speed to disperse liquid droplets N JD Correlation for 6-blade disk impeller (Penney, et al., 1999)

Mixing Lecture 7Slide 12 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Time to Reach Equilibrium Drop Size Time to achieve equilibrium drop size long times 5-20 minutes at lab-scale hours at plant-scale Two parallel process concept (Baldyga & Bourne) Breakup - fast process Coalescence - slow process Rate of Drop Break-up probability of drop going through impeller zone circulation time tank volume important

Mixing Lecture 7Slide 13 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Coalescence - Important Factors Flow field and collision rate Volume fraction of the dispersed phase Viscosity of both phases Condition, age, viscosity and mobility of drop interfaces Presence of particulates, surfactants or suspending agents Coalescence can occur at many locations which complicates interpretation impeller blades baffles liquid surface

Mixing Lecture 7Slide 14 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Population Balance Equation

Mixing Lecture 7Slide 15 Copyright © 2000, A.W. Etchells, R.K.Grenville & R.D. LaRoche. All rights reserved. Separator (Decanter) Design Liquid-liquid Flow into a Cylindrical Vessel Quiet Zone where interface forms Coalescence Layer or Band Assume drops in both phases Settle to coalesce and form interface Avoid interfering with settling process Gravity separation Settling rate given by Stoke’s Law Design for a certain cut size for instance, get all drops above 125 microns Keep (through flow)/(velocity) equal to cut size settling rate